For achieving long distance optical signal transmission, at moderate spectral efficiencies, dual polarization Binary Phase Shift Keying (DP-BPSK) and coherent detection are commonly used. As is known in the art, BPSK encodes a single bit value (“0” or “1”) onto an optical carrier by modulating the carrier phase between two constellation points that are separated by 180°. DP-BPSK achieves a spectral efficiency of 2-bits per symbol period (baud), by independently modulating single bit values onto each of the orthogonal polarization modes of the optical carrier. This is illustrated in FIG. 1, which shows the BPSK constellation mapped onto the Real (Re)—Imaginary (Im) plane of each of the X- and Y-polarizations.
As is known in the art, other modulation schemes enable increased spectral efficiency by encoding increased numbers of bits per baud. For example, Quadrature Phase Shift Keying (QPSK) enables two bits to be encoded on each polarization, and thus four bits per baud for dual polarization QPSK (DP-QPSK), by using a symmetrical 4-point constellation, as may be seen in FIG. 2. Other modulation schemes, such as Quadrature Amplitude Modulation (QAM) achieve even higher numbers of bits per baud by modulating both the phase and amplitude of the optical field. However, as the number of encoded bits-per-baud increases, the Euclidian distance between neighbouring constellation points decreases. For example, in the BPSK constellations shown in FIG. 1, each constellation point is separated from its neighbour by an angle corresponding to 180° in the Re-Im plane. On the other hand, in the QPSK constellations shown in FIG. 2, each constellation point is separated from its neighbour by an angle corresponding to 90° in the Re-Im plane. The reduced separation between adjacent constellation points results in a corresponding decrease in system margin, which limits the maximum signal reach.
Other things being equal, relative system margin varies inversely with the number bits per baud, and both of these parameters are fixed by the encoding scheme. For example, FIG. 3 is a chart schematically showing the relative system margin vs. bits-per-baud for DP-BPSK, DP-QPSK and 16-QAM encoding schemes. In the example FIG. 3, DP-BPSK has the lowest spectral efficiency (2 bits-per-baud) but the highest system margin (and thus signal reach), whereas 16-QAM has the highest spectral efficiency (8 bits-per-symbol) but the lowest system margin.
For an optical communications system having a given baud rate, the specific spectral efficiency and relative system margin of each encoding scheme translates into respective values of bandwidth and signal reach. Accordingly, a network service provider must select an encoding scheme that provides a combination of bandwidth and signal reach that most nearly satisfies the anticipated demand, within the performance capabilities of the network. However, this frequently leads to sub-optimal utilization of the network resources, because the selected encoding scheme will almost invariably have lower spectral efficiency than is permitted by the network performance in order to ensure adequate system margin. Furthermore, if the network service provider wants to change the system margin, for example, they can only do so by changing the encoding scheme. However, this can produce a large step-wise change in both system margin and spectral efficiency, which may also be undesirable.
Various known codes have been used in electrical systems to ensure a minimum number of transitions in a bit sequence. For example, 8B/10B is a line code that maps 8-bit symbols to 10-bit symbols to achieve DC-balance and bounded disparity, and yet provide enough state changes to allow reasonable clock recovery. This means that the difference between the count of 1 s and 0 s in a string of at least 20 bits is no more than 2, and that there are not more than five 1 s or 0 s in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal. Known scrambling techniques make this irrelevant in modern high speed fiber systems.
It is known that block shaping codes, such as the shell codes described in Precoding and Signal Shaping for Digital Transmission; Robert F. H. Fischer; John Wiley & Sons, Inc., 2002, ISBN: 0-471-22410-3, can reduce the average power of the signal by adjusting the probability of occurrence of values of the bits, and efficiently encode fractional bits per Baud. For example, the probability of a certain bit equalling 0 might be 0.75, and the probability of it equalling 1 would be 0.25. With Pulse Amplitude Modulation (PAM), this reduces the average power transmitted by a factor of two. However, when decoding these blocks, one symbol error can produce a large number of bit errors. At the symbol error rates of modern fiber systems (on the order of 5%) this error multiplication offsets the performance gains from the coding. If a symbol error results in a change in the number of bits out of the code, the resulting misalignment can cause a burst of 50% bit errors that persists for thousands of bits.
Forward Error Correction is a well known method for reducing bit error rates. However, the parity calculations for the added redundant bits produce an encoded signal in which the probability of any given bit having a value of ‘1’ reverts to approximately 0.5, even when the input bits deliberately have quite different probability distributions.
Trellis coding has been used in an attempt to overcome the problems of error multiplication and reversion towards 0.5 probability. Symbol level redundancy is included when shaping. Iterative Soft In Soft Out (SISO) decoding across the sequence of symbols is used to gradually reduce the symbol error rate while decoding. This decoding would be very challenging to implement with any significant performance improvement, at the high speeds and high noise levels of modern optical fiber communications systems.
What is desired is a technique that enables spectral efficiency and system margin to be optimized.